Solving multi-manifolds clustering problems that include delineating and resolving multiple intersections is a very challenging problem. In this paper we propose a novel procedure for clustering intersecting multi-manifolds and delineating junctions in high dimensional spaces. We propose to explicitly and directly resolve ambiguities near the intersections by using 2 properties: One is the posi...

We present an approach for building an affine representation of an unknown curved object viewed under orthographic projection from images of its occluding contour. It is based on the observation that the projection of a point on a curved, featureless surface can be computed along a special viewing direction that does not belong to the point’s tangent plane. We show that by circumnavigating the ...

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

In this paper, the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is red...

This has clearly nothing to do with b = 0, the condition that Xo be a stationary line of the quartic. Therefore the cusps of the Steinerian do not lie on the stationary lines, as might be expected from their number -twenty-four. n = 0 is the condition that x2 = 0 be the tangent to the Hessian; then the cusp cannot be obtained by making cl = 0, for then the Hessian has a double point. Putting I ...

— We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our ...

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

Given points P1, P2, . . . , Pn in the plane, we are concerned with the problem of finding a fair curve which interpolates the points. We assume that we have a method in hand, called a basic curve method, for solving the geometric Hermite interpolation problem of fitting a regular C∞ curve between two points with prescribed tangent directions at the endpoints. We also assume that we have an ene...

Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear su...

The Hess screen test was designed by Walter Rudolf Hess in 1908 with subsequent modifications.(1, 2) Hess was a famous neurophysiologist who was awarded the Nobel Prize in 1949 for his research into the functional organization of the vegetative nervous system.(3, 4) The original test used a black screen on which was marked a square-meter tangent scale. The tangent nature of the coordinate lines...